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A Transition to Mathematics with Proofs

Author(s): Michael J Cullinane, PhD, Professor of Mathematics, Keene State University, Keene, New Hampshire
  • ISBN-13: 9781449627782
  • Hardcover    354 pages      © 2013
Price: $177.95 US List
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Developed for the "transition" course for mathematics majors moving beyond the primarily procedural methods of their calculus courses toward a more abstract and conceptual environment found in more advanced courses, A Transition to Mathematics with Proofs emphasizes mathematical rigor and helps students learn how to develop and write mathematical proofs. The author takes great care to develop a text that is accessible and readable for students at all levels. It addresses standard topics such as set theory, number system, logic, relations, functions, and induction in at a pace appropriate for a wide range of readers. Throughout early chapters students gradually become aware of the need for rigor, proof, and precision, and mathematical ideas are motivated through examples.  

Features & Benefits

  • Proof techniques and strategies are thoroughly discussed and the underlying logic behind them is made transparent.
  • Each chapter section begins with a set of guided reading questions intended to help students to identify the most significant points made within the section.
  • Practice problems are embedded within chapters so that students can actively work with a key idea that has just been introduced.
  • Each chapter also includes a collection of problems, ranging in level of difficulty, which are perfect for in-class discussion or homework assignments.
Chapter  1  Mathematics and Mathematical Activity
Chapter  2  Sets, Numbers, and Axioms
Chapter  3  Elementary Logic
Chapter  4  Planning and Writing Proofs
Chapter  5  Relations and Functions
Chapter  6  The Natural Numbers, Induction, and Counting
Chapter  7  Further Mathematical Explorations

Michael J Cullinane, PhD-Professor of Mathematics, Keene State University, Keene, New Hampshire

The following instructor resources are available to qualified instructors for download

ISBN-13: 9781449627782

Image Bank
Slides in PowerPoint Format
Solutions Manual